Explicit constructions of Minimum Storage Regenerating (MSR) codes in the literature are only available for the cases where there are at most $3$ parity nodes, and these existing constructions can only optimally repair a single node failure by accessing all the surviving nodes.
We present two families of explicit high-rate MSR codes for any given code length $n$ and any number of parity nodes $r.$ Our codes can repair any set of failed nodes from any set of helper nodes with the optimal repair bandwidth. The repair procedure of our codes has the optimal error-resilience capability.
We also give another explicit construction of MSR codes with the optimal-access property and nearly optimal node size.

The existing schemes for discrete distribution estimation under locally differential privacy in the literature work well only in the low and high privacy regimes. We propose new optimal schemes and the corresponding estimator which outperform the existing schemes in the medium to high privacy regime. We further prove that our schemes and estimator are asymptotically optimal for any privacy level.

Finally, we give an explicit polar code construction for the successive refinement problem. We also propose new techniques of constructing polar codes that can reduce the construction complexity.